The invention relates to a sensor for the partial pressure of carbon dioxide (pCO2) in particular in vivo or ex vivo, e.g. in or on the surfaces of body tissues or organs, in blood or in the airflow from the lungs, and to a method of measuring pCO2.
Ischemia, localized diminution in blood flow, is the most prevalent cause of death in the western world. Thus for example myocardial infarction, cerebral infarction and other conditions characterised by hypoperfusion to one or more organs are major factors in mortality.
Reperfusion, reversal of ischemia, is frequently possible if an ischemia is detected in time. Thus early detection of ischemia followed by appropriate chemical treatment (e.g. with an agent such as streptokinase, urokinase or t-PA which serves to lyse thrombi or emboli) or surgical intervention can save the affected organ as well as the patient""s life.
While the heart may be monitored continuously for ischemias using an electrocardiograph (ECG), other organs may become severely ischemic and incur irreversible damage before any symptom is detected. Indeed many organs are xe2x80x9csilentxe2x80x9d when it comes to ischemia. The phenomenon of silent myocardial infarction is now well recognised. Furthermore, liver and kidney may be severely ischemic without alerting symptoms before the organ damage is irreversible.
It is known that there is a distinct correlation between pCO2 in or on the surface of an organ and the presence of an ischemia in that organ. During tissue metabolic acidosis, e.g. during the anaerobic metabolism that occurs in an ischemia in any organ or tissue, large quantities of carbon dioxide are formed. CO2 is in practical terms freely cell-membrane permeable and since in the ischemia blood flow to transport away the CO2 is absent or restricted, CO2 build up in the ischemic tissue will occur and pCO2 in or on the ischemic tissue will increase. Generally, in the healthy body, the maximum pCO2 in blood (venous blood) is 7-10 kPa and the maximum PCO2 in healthy (aerobic) tissue is some 1-6 kPa higher, although the maxima may vary from organ to organ, e.g. 8-12 kPa for kidney, 7-11 kPa for liver, 8-12 kPa for intestinal serosa, and 12-19 kPa for intestinal mucosa. Where oxygen supply falls below the critical oxygen delivery level, PC02 values measured in the tissue may rise by 3 to 10 times and the elevated PCO2 levels give a clear indication of anaerobic metabolism and hence, if appropriate, of ischemia.
Sensors for pCO2 are available: however these are generally bulky, often involve relatively complex glass electrodes, routinely do not give stable reproducible readings (i.e. suffer problems of drift), and are sufficiently expensive as to mandate reuse and thus the need to be repeatedly sterilized.
DE-A-2911343 and U.S. Pat. No. 4,324,256 disclose an electrode device for transcutaneous pCO2 measurment with a pH-sensitive measuring electrode in contact with a bicarbonate electrolyte.
There is thus a need for simple, small, and preferably disposable, sensors which can be used generally to determine pCO2, e.g. in order to detect ischemias.
We have now developed a simple sensor particularly suitable for pCO2 measurement, especially as part of a technique for monitoring for ischemias.
Viewed from one aspect therefore the invention provides a carbon dioxide sensor comprising a closed chamber having as a wall portion thereof a substantially water-tight, carbon dioxide-permeable membrane and containing two electrodes, said chamber containing a film of substantially electrolyte-free liquid capable of simultaneously contacting said membrane and both of said electrodes.
By substantially electrolyte-free, it is meant that the liquid has an osmolality no greater than that at 37xc2x0 C. of an aqueous 5 mM sodium chloride solution, preferably no more than that of a 500 xcexcM sodium chloride solution, more especially no more than that of a 10xe2x88x925 to 10xe2x88x926 M HCl solution.
Viewed from an alternative aspect the invention provides a carbon dioxide sensor comprising a first electrode, a second electrode, a carbon dioxide permeable membrane, a liquid in electrical contact with said first and second electrodes and said membrane, means for applying an alternating electrical potential to said first and second electrodes whereby to cause an alternating current in said liquid, and means for generating a signal indicative of the conductance of said liquid, wherein said liquid is reactive with carbon dioxide to alter its conductance and wherein said electrical potential has a frequency of 20 to 10000 Hz, preferably 100 to 4000 Hz.
Viewed from a still further aspect the invention provides a carbon dioxide sensor comprising a first electrode, a second electrode, a carbon dioxide permeable membrane, a liquid in electrical contact with said first and second electrodes and said membrane, and wall means which together with said membrane and said electrodes define a chamber enclosing said liquid such that in the electrical path between said electrodes through said liquid the electrical resistance of said liquid at each of said electrodes is less than in a portion of said liquid in contact with said membrane. This increased electrical resistance relative to the resistance at the electrodes may be achieved by restricting the cross sectional area of the electrical path through the liquid between the electrodes at a zone in which the liquid is in contact with the membrane, e.g. by decreasing the depth of the liquid for a part of the path between the electrodes, and/or by ensuring a relatively large area of contact between each electrode and the liquid.
Preferably the liquid in contact with the electrodes is aqueous and especially preferably it is water, substantially electrolyte-free as defined above. Other solvents that react with CO2 to increase or decrease their conductance, e.g. by the production or neutralization of ions, may likewise be used. In practice, however, deionized or distilled water with or without the addition of a strong acid (e.g. HCl) to a concentration of 0.1 to 100 xcexcM, preferably 0.5 to 50 xcexcM, more especially about 1 xcexcM, has been found to function particularly well. The function of this small addition of acid is generally to maintain the pH of the liquid at 6 or below to avoid significant contributions to conductance by hydroxyl ions and to maintain the linearity of the measurements of PCO2.
The sensors of the invention are provided with or are connectable to an electrical power source arranged to apply an alternating electrical potential across the electrodes with a frequency of 20 to 10000 Hz, preferably 50 to 4000 Hz, more especially 100 to 1200 Hz. At frequencies below 20 Hz, the sensitivity of pCO2 determination is lower due to electropolarization and moreover the instrument response time becomes overly slow, while at frequencies above 10 kHz sensitivity is again less due to stray capacitance effects.
For particularly high accuracy, the potential or current across the electrodes (and hence the resistance or conductance of the liquid between the electrodes) is determined using a lock-in amplifier set to the same frequency as that of the voltage generator.
Furthermore it is preferred to incorporate in the sensor, or in a sensor-plus-detector system, a passive high pass filter (e.g. a capacitor and a resistor) to screen out current with a frequency less than 20 Hz, preferably less than 150 Hz.
The power source may be an AC power source or alternatively a DC source in conjunction with an oscillator, i.e. a combination which together constitutes an AC power source.
The power supply is preferably such that the maximum current density through the liquid at the electrodes is no more than 50 A/m2, preferably no more than 30 A/m2, more preferably no more than 20 A/m2, in particular no more than 10 A/m2, and most preferably about 1 A/m2 or below. Higher current density values of 20 A/m2 or greater should only be used at the higher frequencies, e.g. 1-10 kHz. The smallest maximum current density is determined by detection limits, but values down to 10-8 A/m2 are usable. The smallest maximum current density however will generally be at least 0.1 xcexcA/m2.
By operating at such current densities and voltage frequencies, and by appropriate construction, the sensors of the invention can, unlike the prior art devices, determine the conductance/resistance of the liquid into which the CO2 migrates without any significant loss of accuracy arising as a result of the electropolarization of the electrodes.
Electropolarization effects are considerably reduced by increasing the surface area of the electrodes in contact with the liquid, e.g. by siting the electrodes in wells disposed away from the plane of the membrane or by using non planar electrode surfaces, e.g. rough or textured surfaces. In general therefore it is desirable to have as large a surface area of electrode: liquid contact as possible, as large a surface area of membrane:liquid contact as possible, and as shallow as possible a liquid depth over as much as possible of its area of contact with the membrane. In this way the response time is reduced, electropolarization is reduced, lower frequencies may be used and stray capacitance effects are considerably reduced.
The resistance of the liquid at the membrane and between the electrodes may be increased by the use of means to define liquid channels across the membrane between the electrodes, e.g. by disposing the membrane across or adjacent an insulating chamber wall portion in which such channels are formed, for example by etching. Likewise a porous spacer may be disposed between the membrane and the chamber wall to define the depth of the liquid.
Indeed, such spacers are important to use where, under the pressure conditions experienced in use, the membrane is sufficiently flexible and the liquid depth behind the membrane sufficiently small, for the measured conductance to vary with pressure. However, where a flexible non-CO2 permeable membrane is used, the omission of the spacer or the use of an apertured spacer which allows the membrane to deform under pressure leads to a device in which determination of conductance may be used as a means of measuring pressure, e.g. in vivo.
Thus viewed from a further aspect the invention provides a pressure sensor comprising a first electrode, a second electrode, a flexible membrane, preferably a gas impermeable membrane, and an electrically conductive liquid in contact with said electrodes and said membrane the conductance whereof is altered by pressure induced deformation of said membrane. Such a pressure sensor may be constructed and operated along the same principles as the pCO2 sensors of the invention.
The power source and the detector circuitry may, if desired, be included in the sensor of the invention. In this case, if it is desired that the sensor be wire (ie. lead) free, it will preferably also be provided with means enabling the signal to be detected remotely, e.g. a transmitter, for example a RF transmitter. In this way the sensor may be implanted, for example in an at-risk patient.
The sensors according to the invention are readily produced having a size and configuration particularly suited to measuring pCO2 (or pressure) on the surface of or in an organ, duct or tissue, e.g. brain, heart, liver, kidney, gut or muscle. This is of particular interest as it allows the functioning of the organ, duct or tissue to be monitored, e.g. during and after transplant, in intensive care, following injury, etc. and so allows early detection of ischemias.
Viewed from another aspect the invention provides a method of determining pCO2, e.g. to detect or monitor ischemias, in a human or vascularized non-human animal body (e.g. a mammal, bird or reptile), said method comprising determining a partial pressure of carbon dioxide at a site in said body using a sensor according to the invention, whereby to detect ischemias in said body. The partial pressure determined according to the method of the invention may be a quantified value or it may simply be an indication that pCO2 is above or below one or more threshold values indicative of ischemia or non-ischemia, values which may be varied according to the location of the pCO2 measurement site.
The method of the invention will generally involve determination of pCO2 in blood, on or in an organ, duct or tissue, or in the air flow from the lungs. In the latter case the pCO2 sensor may be inserted into the body or may alternatively be in a hose one end of which is inserted into the body, i.e. within the airways.
The method of the invention may involve a single measurement of pCO2 or, more preferably, may be used for continuous or repeated monitoring, especially of an at-risk patient, for example a patient in intensive care, undergoing or recovering from an organ or tissue transplant operation, assessed as having unstable angina, recovering from a coronary artery bypass operation, suffering trauma (e.g. of skeletal muscle), or suffering from hypovolemia (e.g. shock).
The comparison or threshold values for pCO2 which may be used in the method of the invention may be values detected earlier in a continuous or repeated monitoring of a particular body site using the sensor or they may be values detected for comparable body sites in the healthy, e.g. non-ischemic, body of a comparable subject (e.g. a subject of the same species and sex and similar age and weight).
The primary components of the sensor are an electrode chamber, a CO2-permeable membrane forming at least part of the wall of the electrode chamber, first and second electrodes having surfaces within said chamber (or providing internal surfaces to said chamber), and a liquid (generally substantially electrolyte-free water) in the electrode chamber in contact with the membrane and the first and second electrodes. The sensor includes or is connectable to an AC power supply, a conductance (or resistance) determining means, a signal generating means (which may be part of the determining means) and optionally a signal transmitting means. Moreover the sensor optionally includes surface attachment means by which it may be held in contact with a body surface (e.g. an organ, tissue or duct surface) or surface piercing means by the use of which it may be introduced through a body surface (e.g. an organ, tissue or duct surface).
In one embodiment of the sensor of the invention, a first of the two electrodes has a hollow cylindrical portion and the second is disposed within the hollow cylinder of the first, preferably at or near the axis thereof. The second electrode itself preferably has a solid cylindrical portion disposed within the hollow cylindrical portion of the first electrode. Where the first electrode has a hollow cylindrical portion, this can if desired form a wall of a closed electrode chamber containing liquid and the second electrode and having at least a wall portion provided by the CO2-permeable membrane; however, it is preferred that the sensor has a closed electrode chamber having a further cylindrical wall surrounding, and preferably coaxial with, the two electrodes.
The cylindrical portions of the two electrodes preferably are axially coterminous at the end facing the membrane. They may contact the membrane if it is non-conductive but preferably are slightly displaced from it, e.g. by use of a spacer which may serve to limit or prevent deformation of the membrane.
The first electrode preferably has an outer diameter of the cylindrical portion of 0.8 to 2 mm, more preferably 1.2 to 1.6 mm. The second electrode preferably has an outer diameter of the cylindrical portion of 0.2 to 0.6 mm, more preferably 0.3 to 0.5 mm. The chamber preferably is hollow cylindrical with an internal length of 0.5 to 20 mm, more preferably 5 to 12 mm, and an internal diameter of 0.8 to 2.5 mm, more preferably 1.4 to 2.0 mm.
The membrane is preferably disposed substantially perpendicular to the electrode axis and spaced away from the cylindrical ends of the electrodes, for example by 0.05 to 0.5 mm, preferably by 0.1 to 0.2 mm.
The liquid film preferably covers the membrane to a depth of 0.0005 to 2 mm, more preferably 0.001 to 0.5 mm, when the membrane is horizontal.
Where the sensor is to be used in locations where it cannot be held with the membrane horizontal, the internal depth of the chamber is preferably kept small. In this way the liquid film will fill or almost entirely fill the chamber and so contact the membrane and both electrodes irrespective of the position in which the sensor is held.
The sensor of the invention will preferably include electrical leads from the two electrodes attachable directly or indirectly to a voltage or current applicator and measurement means. Moreover where the sensor is constructed without the liquid film, the chamber will be provided with means for insertion of the liquid, e.g. a sealable inlet port or a pierceable self-sealing substrate such as a rubber stopper. The sensor, with the exception of the membrane which must be exposed at least in part, may if desired be surrounded by a protective biotolerable material, e.g. a casing or a film coating, preferably of a non-conductive material. Likewise, where the sensor is intended for continuous monitoring of blood pCO2, its surface may be coated with an anticoagulant, e.g. heparin. An anticoagulant coating may also be of advantage where the sensor is inserted into an organ and may induce clotting.
Where the sensor is constructed with the liquid film in place, the electrodes are preferably of an inert material such that the resistivity of the liquid will not change significantly with storage. Suitable materials include platinum (especially black platinum), stainless steel, silver, aluminium and carbon, particularly platinum and stainless steel (especially non-magnetic stainless steel where the sensor is to be used in imposed magnetic fields, for example within magnetic resonance imaging apparatus). In general inert electrodes which do not generate solvated ions are preferred. The thickness of the outer electrode and the diameter of the inner electrode will to a large degree depend on the strength of the electrode material used. Both electrodes are preferably of the same material to avoid a DC potential between the electrodes.
The liquid in the sensor may be any liquid capable of changing conductivity on reaction with (e.g. on dissolution therein of) carbon dioxide, e.g. a polar protic solvent capable of dissolving carbon dioxide and thereby producing ions. Water is preferred, however lower alkanols may be used. The liquid however is preferably as free as possible from dissolved ionic species and thus pure, e.g. double distilled, water is most preferred. As indicated above however, to such pure solvents it is desirable to add a small quantity of a strong acid, e.g. to maintain a pH of 6 or below. The quantity of liquid used should preferably be kept as small as possible as in this way the sensor is more rapidly responsive to external changes in pCO2. However the quantity used should preferably be preselected, i.e. so that a group of similar sensors will each contain the same quantity of liquid. In the sensor as manufactured, any gas within the chamber should preferably be essentially CO2 free, e.g. the liquid may have a nitrogen-filled head space. Before use, the sensor will preferably have been sterilised and packed in an airtight, e.g. foil, container to ensure that no accidental exposure to raised levels of CO2 occurs. Also the atmosphere inside the container preferably should be saturated with water vapour to prevent evaporation.
The membrane may be any material which is permeable to CO2, and essentially impermeable to the solvent of the liquid, any electrolyte and water. Teflon(copyright), silicone rubber, polysiloxane, or other insulating polymer films may be used, e.g. at thicknesses of 0.5 to 250 xcexcm. The thicker the membrane, in general the slower the response time of the sensor will be. However the thinner the membrane the greater the risk of non-uniformities or of perforation or other damage. In general, membranes should be thinner for pCO2 measurement in blood or in the airflow. The thicker membranes reduce capacitance effects from ions in organs. In any of the embodiments of the invention, a second (or further) CO2 permeable membrane is preferably mounted adjacent the membrane which contacts the liquid in the sensor. Between the two membranes there may be an air (or other gas) gap (optionally including a gas-permeable spacer) or more preferably a gel especially one containing a sequestering agent (e.g. a chelating agent) that serves to bind anions or cations entering the gap through the external membrane or through holes or defects therein. (In this way drift in long term measurements on organs or tissues may be reduced or avoided). Such a double membrane construction also avoids the capacitance effects of ions in organs and reduces risk of accidental inner membrane perforation and as a result the thinner membranes may be used for pCO2 measurement in organs. Conveniently however the membrane will be about 0.5 to 10 xcexcm, preferably about 1 xcexcm for blood or airflow pCO2 measurement and 1 to 50 xcexcm, preferably 2 to 40 xcexcm for organ pCO2 measurements. It will be appreciated that for detecting ischemia, a response time as long as 10 minutes may be acceptable.
The walls of the chamber of the sensor of the invention may be of any suitable material, e.g. plastics. Preferably the material should be capable of withstanding conditions normally used in sterilisation, e.g. radiation sterilization (for example using xcex3-radiation) or thermal sterilization (for example using temperatures of about 121xc2x0 C. as used in autoclave sterilisation). In the case of thermal sterilization, the liquid will generally be sterile filled into the sensor after sterilization. The walls of the chamber and the membrane may be of the same material, e.g. Teflon(copyright) machined to have self-supporting walls and a thinner gas-permeable end membrane.
In a further, preferred, embodiment the sensor of the invention comprises a CO2 permeable membrane which provides one face of a liquid containing chamber in which the liquid containing volume is defined by the membrane, a first electrode, a second electrode and insulating wall means, the wall means, electrodes and membrane defining (i) a small cross-sectional area of the liquid (across the direction of current flow) at a membrane contacting portion of the liquid, (ii) a large surface area membrane-contacting portion of the liquid and (iii) relatively large electrode:liquid contact portions. This may be achieved by placing the electrodes in wells in an insulator (which may or may not be provided with channels between the wells) with a central insulator portion which is more closely adjacent the membrane such that liquid resistance is higher in a membrane-adjacent portion of the electrical flow path than in the electrode adjacent portions. For this purpose, the electrodes may conveniently be formed as layers within a sandwich electrode:insulator construction or as wires or deposits placed in grooves or indentations in an insulator substrate.
The sensor device of the invention can thus be made small enough for insertion into a respiratory hose, into the vasculature or into or onto the surface of an organ, tissue or duct; it is cheap and simple and may have single-use application (i.e. it can be disposable) or alternatively it may be sterilised and reused. The response time to pCO2 changes is rapid (e.g. 10 minutes, preferably 5 minutes, or more preferably 30 seconds, or less) and problems of drift encountered with conventional blood gas electrodes are avoided. The device is thus well-suited for the clinical environment.
Where the sensor is to be reused, the membrane and electrodes are preferably separable to permit replacement of the liquid. Thus for example the membrane may be replaceable, e.g. taking the form of a disc disposed between the body and a sealingly engageable and removable end cap of the chamber. In this embodiment, between uses, the end cap and membrane will be removed, the solvent replaced, and the end cap and membrane disc (either as two components or an integral unit) replaced. During or after this procedure, the sensor will be sterilized. More preferably however the sensor will be a single-use, disposable device.
For in vivo measurement of pCO2 (except for in vivo blood gas measurements) no widely commercially available technique has yet been developed. Several techniques have been tried in animal experiments (ISFET electrodes, infrared absorption and others), but all of them have shortcomings. (ISFET electrodes have been used in humans but without satisfactory results). Among weaknesses are size, drifting and high cost of manufacturing. In contrast the sensors of the invention are inexpensive to produce, will have minimal drifting and with proper quality of de-ionized water, calibration may not be necessary. Using a small volume of water and preferably carbonic anhydrase, they will be fast enough for measuring end-expiratory pCO2. The sensors can be small and can be disposed in the main stream in a respirator hose. Consequently, there will be no need to suction out gas from the ventilator hoses as is now done with most techniques. This is a definite advantage, particularly in the monitoring of children whose respiratory volumes are small. Thus the sensors of the invention have the potential of being applicable for in vitro, in vivo and end-expiratory measurements of pCO2. They can both be used for ventilatory monitoring, intravascular pCO2 measurement and for detection of ischemia at the organ level.
Besides in vivo an ex vivo uses, the sensors of the invention may be used in other situations where pCO2 measurement is desired, in particular uses not associated with animate test subjects, e.g. in vitro measurements of pCO2 in gases or liquids, for example drinks or effluent gases. In further aspects the invention provides a method of determining pCO2 or pressure in such in vitro uses using sensors according to the invention.
It is especially preferred that the sensors of the invention be applied to the surface of a tissue, duct or organ of interest to determine pCO2 for that tissue, duct or organ. This is feasible since CO2 diffuses out of tissues, ducts and organs such as the heart, liver, kidney, brain, gut and muscle. For these purposes it is desirable that the sensor include surface attachment means (e.g. a flexible or perforated flange which may be sutured to the organ, tissue or duct surface; a flexible tissue-adhesive carrying flange; an adjustable clip; a flexible barb etc). In this embodiment, the electrode chamber is preferably disc-shaped with the CO2 permeable membrane on one of the faces of the disc. Such pCO2 sensors are in themselves novel and form a further aspect of the invention. Viewed from this aspect the invention provides a pCO2 sensor having a disc-shaped electrode chamber one face of which is provided at least in part by a CO2 permeable membrane, said sensor further comprising surface attachment means.
Where alternatively the sensor is to be inserted through a body surface (e.g. an organ, tissue or duct surface) it will conveniently be provided with surface piercing means, for example having the electrode chamber in the shaft of an elongate sharp-ended sensor. Such sensors are also novel and form a further aspect of the invention. Viewed from this aspect the invention provides a pCO2 sensor having an elongate body portion with sharp body surface piercing means at a first end thereof and containing spaced away from said first end an electrode chamber at least a portion of an exposed wall whereof is provided by a CO2 permeable membrane.
The sensors of the invention are relatively inexpensive and so, unlike prior art sensors, may be single-use devices. Moreover the electrode chamber can be made extremely small without difficulty (unlike the prior art glass electrode containing sensors for which miniaturization poses insuperable impedance problems).
The mechanism by which pCO2 is determined using the sensor device of the invention is straightforward. In a pure protic solvent, e.g. water, the electrical resistance is high because of the paucity of ionic species. Addition of CO2 results in formation (with water) of H+ and HCOxe2x88x923 ions and thus a reduction in the electrical resistance. Since the only factor responsible for reduction in resistance in the sensor is CO2 passing through the membrane, the change in resistance enables pCO2 to be measured. (In the pressure sensor of the invention on the other hand the change in resistance arises from the change in cross sectional area of the electrical path through the liquid due to pressure induced deformation of the membrane).
From the equilibrium constant for the H2O+CO2 to H++HCOxe2x88x923 equilibrium, CO2 concentration is equal to xcex1pCO2 (where xcex1 at 25xc2x0 C. is 0.310). The electrical conductivity for protons is GH+=349.8 S.cm2/mol, that for hydroxyls is GOHxe2x88x92=198.3 S.cm2/mol and that for bicarbonate is GHCO3xe2x88x92=44.5 S.cm2/mol. The concentrations of H+ and OHxe2x88x92 vary inversely, and the concentrations of H+ and HCO3xe2x88x92are directly proportional to pCO2. The total conductance of the solution is thus effectively proportional to pCO2 since the contribution of OHxe2x88x92 is minimal. The conductivity of the solution Gsolution is thus given by
Gsolution=xcex8H+[H+]GH++xcex8OHxe2x88x92[OHxe2x88x92]GOHxe2x88x92+xcex8HCOxe2x88x923[HCO3xe2x88x92]GHCO3xe2x88x92
where xcex8Hxe2x88x92, xcex8OHxe2x88x92 and xcex8HCO3xe2x88x92 are the activity coefficients for the three ionic species.
Table 1 below shows, by way of example, measured pCO2 and pH values and corresponding calculated values for H+, OHxe2x88x92 and HCO3xe2x88x92 concentrations showing the increase of H+ and HCO3xe2x88x92 with increasing pCO2.
The electrical conductivity is measured in the solvent film in the sensor of the invention. This can be done by applying a constant voltage (or current) to the electrodes and measuring the current (or voltage) changes which correspond to changes in conductivity as CO2 enters the solvent through the membrane. Preferably however an alternating sine wave function voltage with a constant peak value is applied and the voltage drop over the two electrodes is measured. The solution conductivity is then equal to the current passed through the electrode divided by the voltage drop over the two electrodes.